Journal of Optimization Theory and Applications

, Volume 155, Issue 1, pp 239–251 | Cite as

On Geodesic E-Convex Sets, Geodesic E-Convex Functions and E-Epigraphs

  • Akhlad Iqbal
  • Shahid Ali
  • I. Ahmad


In this paper, we introduce a new class of sets and a new class of functions called geodesic E-convex sets and geodesic E-convex functions on a Riemannian manifold. The concept of E-quasiconvex functions on R n is extended to geodesic E-quasiconvex functions on Riemannian manifold and some of its properties are investigated. Afterwards, we generalize the notion of epigraph called E-epigraph and discuss a characterization of geodesic E-convex functions in terms of its E-epigraph. Some properties of geodesic E-convex sets are also studied.


Geodesic E-convex sets Geodesic E-convex functions Geodesic E-quasiconvex function E-epigraphs Riemannian manifolds 



The authors are highly thankful to anonymous referees and the editor for their valuable suggestions/comments which have contributed to the final preparation of the paper.


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© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of MathematicsAligarh Muslim UniversityAligarhIndia
  2. 2.Department of MathematicsBITS Pilani Hyderabad CampusHyderabadIndia
  3. 3.Department of Mathematics and StatisticsKing Fahd University of Petroleum and MineralsDhahranSaudi Arabia

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